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Vector identity proof in general curvilinear coordinates

  1. May 19, 2015 #1
    1. The problem statement, all variables and given/known data

    Need to prove that:


    phys1.jpg

    ,b means partial differentation with respect to b, G is the metric tensor and Γ is Christoffel symbol.

    I think I could proceed with this quite well if I could understand the hint given, that I should lower the index j.

    2. Relevant equations

    am=Gmjaj

    3. The attempt at a solution

    For the first member on the left I could write

    GmjGjkkkmk=∂k

    and else than that it should stay the same

    For members on the right, lowering j would give me

    vα(vj,αjαβvβ)

    However, what should I do with the second member on the left? And I am told that this one is the important one.
     
  2. jcsd
  3. May 24, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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